Complex numbers. Where in life do we use them?

Question

I honestly don't understand the logic of learning algebra. Where would we ever use complex numbers?

Answer 1

complex numbers are used all the time when describing oscillations. I am in aerospace engineering and we use the complex plane to determine how much the plane is damped and what the frequency of oscillations would be.

For example, if the number is -100000 +- i, then the system decays very very quickly, but doesn't really oscillate. but if the number is -1 +- 10000000000000i, then it oscillates a lot and it takes a really really long time for it to decay and get damped and become constant.

This is used mainly when solving 2nd order differential equations. The most famous example is a mass-spring-damper system. The real part is related to how quickly it is damped and the imaginary part is related to the frequency of oscillations. Many things are described by oscillations and 2nd order differential equations. There are also other uses, but those are some of the major ones.

An aerospace example is if you're flying in a plane, and you get some disturbance (say, some turbulence), then you want the effects of that disturbance to go away quickly. There is a differential equation that describes the motion of the plane and if the solution of the differential equation has a really big imaginary part, then that means the plane will continue to oscillate (move up and down) for a long time. Ideally, you would want the real part to be high and the imaginary part to be low so it would go back to its normal condition quickly and not oscillate much.

A lot of the stuff you learn in high school seems really really useless, but almost all of it is actually used somewhere in real life for something.

I hope that helps in a way. Even though that's probably more information than you wanted.

btw, algebra is one of the most useful courses ever. I didn't like it at all, but it comes up everywhere. especially matrices and vectors and stuff.

Almost everything can be described by some form of Ax=b, where A is a matrix and x and b are matrices.

Anyways, laterz

Answer 2

Most people will never use them. However, one place they are virtually indispensible is electronics. Quite often currents and other measurements in AC circuits can be described only in terms of complex numbers. I defy you to understand how to apply Ohm's Law to parallel RLC AC circuits without understanding complex numbers! In fact, most of the electronic devices existing today would never have been developed if there were no complex number theory.

As far as "why learn algebra?" goes, don't knock it until you've learned calculus and what it can do. I'm sure you'll see plenty of applications there.

Answer 3

In Electrical Systems Complex Numbers can be used to the Phase Angle of the Voltage or Current

Answer 4

Probably never. Complex mumbers were created for the purpose of having a solution to all quadratics and other math applications. In real life, you might never see them again.

Answer 5

You are better off not confronting abstract math concepts with the test of where you are going to use this. If you want everything that you study to have daily use, get a job in a hardware store.

Answer 6

I know that they are used when studying electronics and quantum theory in physics, and they have use in pure mathematics. For instance, Euler's identify states that e^(iπ) = -1. But most of their uses are relatively obscure, and you probably won't use them much.

Answer 7

They are used when you study alternating currents in Electricity
Electrical engineers use them currently

Answer 8

never actually